Ch. 2.1 Conditional Statements HMWK : p.75, #s 10 – 50 even. Game Plan: Today I will be able to 1.Analyze conditional statements 2.Utilize Postulates.

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Ch. 2.1 Conditional Statements HMWK : p.75, #s 10 – 50 even. Game Plan: Today I will be able to 1.Analyze conditional statements 2.Utilize Postulates. Warm-up: Your parents ask you to fertilize the lawn. It is a square plot that is 22 ft. on each side and it has a square cement fountain in the center that is 6 ft on each side. What is the area of the lawn that you will fertilize? Be sure to sketch the lawn, and label the dimensions. 448 ft 2

Ch. 2.1 Conditional Statements Two part statement If-then form “if” – hypothesis “then” – conclusion P  Q If you study for at least three hours, then you will pass the test. Hypothesis Conclusion

Ch. 2.1 Conditional Statements Conditional Statements cont. Counterexample: statement to prove conditional statement false Converse: Switching the hypothesis and conclusion. – –Q  P Inverse: the negation (negative or opposite) of the hypothesis and conclusion – –~P  ~Q Contrapositive: the negation of the hypothesis and conclusion of the converse. – –~Q  ~P Equivalent Statements: two statements are both true or both false – –P  Q is equivalent to ~Q  ~P – –~P  ~Q is equivalent to Q  P

Ch. 2.1 Conditional Statements What does this mean? … If you study for at least three hours, then you will pass the test. P  Q Converse: If you passed the test, then you studied for 3 hours. Q  P Inverse: If you did not study for at least three hours, then you did not pass the test. ~P  ~Q Contrapositive: If you did not pass the test, then you did not study for 3 hours. ~Q  ~P

Ch. 2.1 Conditional Statements Postulates 5. Through any two points there exists exactly one line. 6. A line contains at least two points. 7. If two lines intersect, then their intersection is exactly one point. 8. Through any three noncollinear points there exists exactly one plane.

Ch. 2.1 Conditional Statements More Postulates… 9. A plane contains at least three noncollinear points. 10. If two points lie in a plane, then the line containing them lies in the plane. 11. If two planes intersect, then their intersection is a line.

Ch. 2.1 Conditional Statements Wrap up … 1.Write a conditional statement. 2.Switch with your neighbor … 3.Write the following of your neighbors conditional statement ConverseConverse InverseInverse ContrapositiveContrapositive